INDUCTANCE AND CAPACITY 391 



It will be assumed that the bridge arms have impedances 

 Z M , Z N , Z x , Z P , and Z G and are traversed by sinusoidal cur- 

 rents. All the impedances are expressed in symbolic notation. 

 The mesh currents will be taken as indicated. As cognizance 

 must be taken of their phase relations, these currents must 

 also be expressed symbolically and referred to the same axis, 

 for instance, I B - Applying Kirchhoff's laws, for the X mesh, 



X (Z M + Z G + Z N ) - (X + Y) Z G - I B Z N = 0, 

 for the (X + F) mesh, 



(X + Y)(Z X + Z P + Z G ) - XZ G - I B Z P = 0. 

 Solving for F, the current through the detector, 



v I B (Z P Z M - Z N Z X ) 



" Z Q (Z X + Z P + Z M + Z N ) + (Z M + Z N )(Z X + Z P ) 



If the detector and generator be interchanged, the value of the 

 detector current becomes 



V- I B (Z N Z X Z P Z M ) 



' Z G (Z x + Zp + Z M + Z N ) + (Z M + Z x ) (Z N + Z P ) ( ^ } 



The condition for no current in the detector is 



Z N Zx = Z P Z M - (26) 



Compare the above with corresponding deduction for the Wheat- 

 stone bridge, page 183. 



The generator used as a source of power should give a sinusoidal 

 e.m.f. wave. 



The ratio arms (M and N) may be non-inductive resistances, 

 highly inductive resistances, or perfect condensers. Bridges 

 with highly inductive ratio arms have been used by Giebe in 

 inductance measurements 20 and by Grover 16 in measurements 

 of the capacity and power factor of condensers. 



The detector may be either a telephone or a vibration gal- 

 vanometer. At low frequencies the latter is to be preferred, for 

 it is a tuned instrument responding freely to currents of only 

 one frequency. With it an accurate balance may be obtained 

 even though the currents are not exactly sinusoidal. Electro- 

 static disturbances are also avoided. 



As the maximum frequency obtainable with the vibration 



